It doesn't have to be yuchy tar - any of the white or silver, paint on, rubber roof coatings should do the job, assuming it actually is the roof. You can get mobile home roof coatings such as Kool Seal at most hme or hardware stores.
But if the leak is in a seam at the edge or around some raised projection like a air conditioner, skylight, or antenna, painting on a roof coat may still not get it. Only caulk applied in the right place will resolve those. Ditto if the leak is high in a sidewall, such as the awning mount mentioned earlier here. Water can travel a long way inside a roof before exiting through an opening or seam in the interior.